Question 1151809: using truth tables, decide if each argument is valid.
p ∨ ∼q
∼q → p
∴ p
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
premise1 = p v ~q
premise2 = ~q -> p
conclusion = p
p is some logical statement that can be either true (T) or false (F)
q is also either T or F
The first two columns of the table below represent the four possible ways to have a T and F combo
The third column ~q represents the negation of column q. This is the opposite of the q column.
The fourth column has p and ~q in a disjunction. A disjunction is only false when both parts are false; otherwise, it is true.
The ~q -> p column is only false when ~q is true while p is false, ie in the form T -> F; otherwise it is true.
The last column is just a copy of the first column. It's to help set up the conclusion which is often the last column.
Truth Table
| p | q | ~q | p v ~q | ~q -> p | p |
| T | T | F | T | T | T |
| T | F | T | T | T | T |
| F | T | F | F | T | F |
| F | F | T | T | F | F |
An invalid argument would be if all the premises were true and they lead to a false conclusion. That doesn't happen here because the first two rows have a true conclusion while the last two rows have not all premises being true.
So the argument is valid.
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